Department of Mathematics
Final Exam
Mathematics 9A  First Year of Calculus
Sample 3
Instructions:
This exam has a total of 200 points. You have 3 hours.
You must show all your work to receive full credit. You may use any result
done in class. The points attached to each problem are indicated beside the
problem. You are not allowed to use books, notes, or calculators. Answers
should be written as
p
2
as opposed to
1
:
4142135
:::
.
1. Compute
(a) (10 points)
lim
x
!
4
p
x
+5
3
x
4
(b) (10 points)
lim
x
!
0
sin
2
x
3
x
lim
x
p
x
2
+2
2
x
1
2. (20 points) Let
f
(
x
) =
(
x
2
2
x
3
x
3
if
x
6
= 3
5
if
x
= 3
:
:
For what values of
x
is
f
continuous?
3. Compute
dy
dx
.
(a) (5 points)
y
=
5
p
x
+
p
x
(b) (5 points)
y
=
x
2
+3
x
2
1
±
3
(c) (5 points)
y
=
x
cos(
p
x
+ 1)
(d) (5 points)
y
= [sin(
x
2
+ 1)]
3
4. (20 points) Find an equation of the tangent line to the curve
x
2
(
x
y
) =
x
2
y
2
at the point
(1
;
1)
.
1
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 Spring '09
 Nouh
 Calculus, Derivative, Mathematical analysis, Convex function, Riverside Department of Mathematics

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